Law of Equipartition of Energy
According to the law of equipartition of energy, for any dynamic system in thermal equilibrium, the total energy for the system is equally divided among the degree of freedom.
We know that whenever the molecules of a gas collide, they share their energies and when thermal equilibrium is reached, the average energy of each molecule is the same. The law of equipartition of energy, first deduced by Maxwell in 1869 and later on, improved by Boltzmann, showed as to how much should be the average energy of a gas molecule. This law is remarkable as it is applicable to large collections of atoms, electron and molecules. We shall, however, confine ourselves to its application to the molecules of a gas.
According to this law, for any system in thermal equilibrium, the total energy is equally distributed among its various degree of freedom and each degree of freedom is associated with energy ½ kT.
k = 1.38 x 10⁻²³ J/ K.
T = Absolute temperature of the system.
At a given temperature T, all ideal gas molecules no matter what their mass have the same average translational kinetic energy 3/2 kT.
We are also measuring the average translational kinetic energy of its molecules. At same temperature gases with different degrees of freedom will have different average energy or internal energy namely f/2 kT (f is different for different gases).
Using the law of equipartition of energy, the molar specific heats can be determined and the values are in agreement with the experimental values of specific heats of several gases. The agreement can be improved by including vibration modes of motion.